Problem: Simplify the following expression: $k = \dfrac{-6r^2 - 78r - 252}{r + 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ k =\dfrac{-6(r^2 + 13r + 42)}{r + 6} $ Then we factor the remaining polynomial: $r^2 + {13}r + {42} $ ${6} + {7} = {13}$ ${6} \times {7} = {42}$ $ (r + {6}) (r + {7}) $ This gives us a factored expression: $\dfrac{-6(r + {6}) (r + {7})}{r + 6}$ We can divide the numerator and denominator by $(r - 6)$ on condition that $r \neq -6$ Therefore $k = -6(r + 7); r \neq -6$